A car is driven east for a distance of 54 km, then north for 32 km, and then in a direction 28° east of north for 27 km. Draw the vector diagram and determine the total displacement of the car from its starting point.

8 years ago
Assumption:

Let us assume that the vector represents the eastward motion of the car with a magnitude of , the northward motion of the car is given by vector with a magnitude of 32 km while the east of north motion by vector with a magnitude of
27 km.
The figure below shows the vector diagram of the Car’s motion:

In vector , there is no vertical component but only the horizontal component along the east with magnitude 54 km. Therefore vector is:

For vector , there is no horizontal component as it describes the northward motion of the car, along the unit vector .
The magnitude of the vertical component of the car is 32 km, therefore vector can be written as:

From the vector diagram above, it is clear that the horizontal component of vector points in the direction of unit vector . Therefore the horizontal component of vector is .
27 km sin (28°)
The vertical component of the vector points northward, along the unit vector , therefore the component is.27 km cos(28°) .
Therefore vector is:

The magnitude of total vertical displacement (say sv) of the car along the north is the sum of vertical component of vector , the vertical component of vector and the vertical component of vector .
Since vector does not have a vertical component, we add the vertical component of vector and , to obtain the magnitude of displacement sv as:

The magnitude of total horizontal displacement (say sh) of the car along the east is the sum of horizontal component of vector , the horizontal component of vector and the horizontal component of vector .
Since vector does not have a horizontal component, we add the horizontal component of vector and , to obtain the magnitude of displacement sh as:

The magnitude of net displacement (say s) of the car can be calculated using the magnitude in equation (1) and (2) as:

Rounding off to two significant figures
s = 87 km
Therefore the magnitude of displacement of the car during his journey is 87 km .